Statistics MCQs, Data Analysis, Stat Software
Correlation Analysis using Pearson’s Correlation Coefficient, Spearman’s Rank correlation, Measure of the linear relationship between quantitative variables, strength, and direction of relationship, Coefficient of correlation
The coefficient of correlation is a statistic used to measure the strength and direction of the linear relationship between two Quantitative variables. Properties of Correlation Coefficient The following are some important Properties of Correlation Coefficient. Hence, $r_{YX}, b_{YX}$, and $b_{XY}$ have the same sign. Theorem: Correlation: Independent of Origin and …
Consider the following data for the illustration of the detection of heteroscedasticity using the Spearman Rank correlation test. The Data file is available to download. Y X2 X3 11 20 8.1 16 18 8.4 11 22 8.5 14 21 8.5 13 27 8.8 17 26 9 14 25 8.9 15 …
Covariance and Correlation are very important terminologies in the Subject of Statistics. Covariance measures the degree to which two variables co-vary (i.e. vary/change together). If the greater values of one variable (say, $X_i$) correspond with the greater values of the other variable (say, $X_j$), i.e. if the variables tend to …
We know that the ratio of the explained variation to the total variation is called the coefficient of determination which is the square of the Correlation Coefficient Range lies between $-1$ and $+1$. This ratio (coefficient of determination) is non-negative, therefore denoted by $r^2$, thus \begin{align*}r^2&=\frac{\text{Explained Variation}}{\text{Total Variation}}\\&=\frac{\sum (\hat{Y}-\overline{Y})^2}{\sum (Y-\overline{Y})^2}\end{align*} …